Animating Curves for Arms and Legs
When I do 2D stuff, I use armatures, which work well when the mesh has evenly distribuited quads. In my example I created the line with 4 vertices, then I added some loop cuts until they were evenly distribuited, then I added 2 loop cuts near every joint, then I made the bones to be bendy bones with 2 segments each, playing with curve Y in and out settings.

The rounded cap is obtained by simply adding a subsurf modifier (level 3), which has to be set after the armature modifier. Enable the Armature "preserve volume" option for better results.


 

Watch Nathan Vegdahl's free YouTube humane rigging course, in some of the first lessons he explains some useful rigging tricks fro 2D animation.